What is angular velocity and how is it related to circular motion?

Angular velocity is the rate of change of angular displacement with respect to time.

In circular motion, an object moves along a circular path with a constant speed. However, its direction changes constantly, resulting in a continuous change in its angular displacement. Angular velocity is the measure of this change in angular displacement per unit time. It is a vector quantity and is expressed in radians per second (rad/s).

The direction of the angular velocity vector is perpendicular to the plane of motion and follows the right-hand rule. If the object is moving clockwise, the angular velocity vector points downwards, and if it is moving anticlockwise, the vector points upwards.

Angular velocity is related to linear velocity, which is the rate of change of linear displacement with respect to time. The two are related by the radius of the circular path. Specifically, the linear velocity is equal to the product of the radius and the angular velocity. This relationship is expressed as v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity.

In summary, angular velocity is a measure of the rate of change of angular displacement, and it is related to circular motion through the radius of the circular path.